Avoiding the Finite Difference Sensitivity Analysis Deathtrap by Using the Complex-step Derivative Approximation Technique

In this paper, the complex-step derivative approximation technique will be used for calculating local sensitivity functions. This technique is compared to the finite difference approximation, probably the most used local sensitivity analysis technique. For this comparison, 4 biotechnological models with varying model complexity were used. A well known problem of the finite difference approximation is the choice of a suitable perturbation factor in order to avoid non-linear model effects or numerical errors due to the subtraction of almost equal numbers. The main advantage of the complex-step derivative approximation technique is that it is not susceptible to errors introduced by small perturbation factors, ruling out the entire search for optimal perturbation factors. However, the main disadvantage is an important execution time increase for large models.